1. Field of the Invention
The present invention relates to navigational systems. Specifically, the invention relates to methods of compensating for bias drift in gyroscopes used in vehicle navigational systems having a dead reckoning component, and subsequently correcting heading and position errors resulting from the gyroscope bias and gyroscope bias drift.
2. Description of Related Art
Numerous automotive navigational systems have been developed in recent years for such applications as providing real-time driving directions and providing emergency services for automobiles. These navigational systems typically include a satellite-based positioning system or a xe2x80x9cdead reckoning systemxe2x80x9d (DRS), or a combination of the two. In a dead reckoning system, the heading and position of a vehicle are determined using sensors such as gyroscopes and odometers. Typically, automobile navigational and positioning systems use a DRS having an interface between a transmission odometer (for tracking speed and distance) and a gyroscope (to track the vehicle""s heading). Dead reckoning systems are often used in tandem with a satellite-based navigational system such as a Global Positioning System (xe2x80x9cGPSxe2x80x9d).
The Global Positioning System (GPS) is a satellite-based radionavigation system developed and operated by the U.S. Department of Defense. GPS allows land, sea and airborne users to constantly determine their three-dimensional position, velocity, and time anywhere in the world with a precision and accuracy far better than other radionavigation systems currently available. The GPS consists of three segments: user, space and control. The user segment consists of individual receivers, processors, and antennas that allow land, sea or airborne operators to receive GPS satellite broadcasts and compute their precise position, velocity and time from the information received from the satellites. Use of GPS receivers in automotive navigation, emergency messaging, and tracking systems is now widespread. GPS receivers have been miniaturized to comprise only a few integrated circuits for individual use.
The space segment consists of 24 satellites in orbit around the Earth and positioned so that at any time between five and eight satellites are xe2x80x9cin viewxe2x80x9d to a user at any particular position on the surface of the earth. These satellites continuously broadcast both position and time data to users throughout the world.
The control segment consists of five land-based control and monitoring stations located in Colorado Springs (master control station), Hawaii, Ascension Island, Diego Garcia, and Kwajalein. These stations monitor transmissions from the GPS satellites as well as the operational status of each satellite and its exact position in space. The master ground station transmits corrections for the satellite""s position and orbital data back to the satellites. The satellites synchronize their internally stored position and time with the data broadcast by the master control station, and the updated data are reflected in subsequent transmissions to the user""s GPS receiver, resulting in improved prediction accuracy.
In general, a minimum of four GPS satellites must be tracked by the receiver to derive a three-dimensional position fix. The fourth satellite is required to solve for the offset between the local time maintained by the receiver""s clock and the time maintained by the GPS control segment (i.e., GPS time); given this synchronization, the transit time measurements derived by the receiver can be converted to range measurements and used to perform triangulation. Navigational systems based solely on GPS, therefore, generally do not work well in dense city environments, where signal blockage and reflection by tall buildings, in addition to radio frequency (RF) interference, often occurs. GPS accuracy also suffers in situations where the GPS satellites are obscured from the vehicle""s field of view, e.g. when the vehicle is in a tunnel or dense foliage environments.
In combination systems, such as navigational systems having both DR and GPS components, heading and position data from each component are used to compensate for measurement errors occurring in the components. The dual component system also provides a backup system in the event that one component fails, for example, DRS provides continuous heading and position information even when the GPS satellites are obscured from the view of the vehicle, and thus no reliable GPS information is available.
Dead reckoning systems, however, are only as accurate as their component sensors, which are often low-cost and low-fidelity. For example, the gyroscopes typically used in dead reckoning systems are vibrational gyroscopes, which are known to have severe performance limitations. The performance of low-cost gyroscopes is directly correlated to gyroscope bias, a measure of a gyroscope""s deviation from an ideal or perfect gyroscope, and bias drift, the rate of change of the bias resulting from changes in environmental conditions over time. Gyroscope bias is determined by the gyroscope""s reading at zero angular rate, which a perfect gyroscope would read as zero. Gyroscope biases can be as large as several degrees per second for automotive-quality gyroscopes.
In the case of the commonly used vibrational gyroscope, a vibrating beam is used to determine heading changes. Over time, the vibrational characteristics of the beam change and these changes result in changes in the measured angular rate, even when there is no rotation of the beam, thus producing the gyroscope bias drift. Significantly, bias drift produces a position error that grows quadratically with distance-traveled for a vehicle moving at a constant speed.
The most significant factor in gyroscope bias drift is temperature change. Changes of no more than a fraction of a degree in temperature can produce significant shifts in the gyroscope bias. For example, a bias of only 0.055 deg/sec produces a position error of 5% of distance-traveled, or 50 meters, after 1 kilometer of travel and 25% of distance-traveled, or 1.25 kilometers, after 5 kilometers of travel. While the position error can be compensated for using GPS under conditions where a minimum of four satellites are in view of the vehicle, the error cannot be effectively compensated for during periods of GPS outage such as occur in tunnels or dense foliage environments. It is therefore desirable to have methods for correcting heading and position errors in dead reckoning systems resulting from the temperature dependence of gyroscope bias and gyroscope bias drift.
Compensation for temperature-dependent bias drift is further complicated because the system exhibits a hysteresis effect. In a hysteretic system, the dependent variable (gyroscope bias) is not only a function of the independent variable (temperature), but is also a function of the time history of the dependent variable. Therefore, the system is not perfectly reversible. If a gyroscope is subjected to a temperature change and then subjected to a temperature change of the same rate and magnitude in the reverse direction, the temperature dependence of the bias can be different along the forward and reverse paths.
Methods for correcting heading and position errors in vehicle navigation systems, including methods of compensating for gyroscope bias, are known in the art. Most existing methods, however, use estimated positions determined by the dead reckoning or GPS components to correct for gyroscope bias. Other existing methods rely on predetermined calibration curves for gyroscope bias and bias drift. Further alternative existing methods are useful only for high-end gyroscopes that are too expensive for routine use in consumer automotive positioning systems.
U.S. Pat. No. 3,702,477 to Brown teaches a Kalman filter method for estimating the gyroscope bias of an aircraft-quality inertial measurement unit comprising at least three gyroscopes and three accelerometers, using position error measurements constructed from the Navy Navigation Satellite System, a predecessor to GPS.
U.S. Pat. No. 3,702,569 to Quinn et al. discloses a hardware modification for removing the relatively large, fixed offset that appears in high-precision gyroscopes. The modification is applicable to precision gyroscopes typically costing several thousand dollars, rather than the low-cost gyroscopes used in vehicular navigation and positioning systems.
U.S. Pat. No. 4,303,978 to Shaw et al. teaches one-time factory calibration of high-end gyroscopes based upon a predetermined calibration curve. Such methods are not useful for low-cost gyroscopes where calibration curves are not readily determinable.
U.S. Pat. Nos. 4,537,067 and 4,454,756 to Sharp et al. teach compensation for temperature-dependent gyroscope bias drift by controlling the temperature of the gyroscope environment and estimating gyroscope bias using inertial navigation system (INS) position data.
U.S. Pat. No. 4,987,684 to Andreas et al. teaches a method of compensating for gyroscope drift in an inertial survey system by using position updates generated by a Kalman filter method.
U.S. Pat. No. 5,194,872 to Musoff et al. teaches a method of compensating for gyroscope bias in an aircraft inertial navigation system (INS) by using output from a set of redundant gyroscopes to correlate bias.
U.S. Pat. No. 5,278,424 to Kagawa teaches a method of compensating for gyroscope using position information obtained from a digital map database.
U.S. Pat. No. 5,297,028 to Ishikawa and U.S. Pat. No. 5,527,003 to Diesel et al. teach a method of compensating for temperature-dependent gyroscope bias by determining and applying a calibration curve for gyroscope bias as a function of temperature.
U.S. Pat. No. 5,416,712 to Geier et al. discloses use of a Kalman filter method for correcting future heading and position error growth, based upon an assumption of constant gyroscope bias drift rate between position updates.
U.S. Pat. No. 5,505,410 to Diesel et al. and U.S. Pat. No. 5,574,650 to Diesel teach a method for correcting the east component of gyroscope bias from measurements of cross-track velocity error made when an aircraft is taxing.
U.S. Pat. No. 5,543,804 to Buchler et al. teaches a method for combining GPS and inertial navigation systems data for improved attitude determination accuracy that incorporates a Kalman filter method for estimating the gyroscope biases of the INS.
U.S. Pat. No. 5,583,774 to Diesel teaches calibration of gyroscope bias using GPS position and velocity data.
There remains a need in the art for methods compensating for temperature-dependent gyroscope bias drift in low-cost, vehicular navigation an and for the position and heading errors that result from gyroscope bias and gyroscope bias drift, as well as devices incorporating such compensation methods.
The present invention solves the problems of the prior art by providing methods and apparatuses for compensating for temperature-dependent drift of bias in a heading sensor used in a dead reckoning system for providing a vehicle heading and position.
In a first aspect, the invention provides methods that use a Kalman filter to generate a calibration curve for the rate of heading sensor bias drift with temperature change. The Kalman filter calculates coefficients for a model of bias drift rate versus temperature at each point where the vehicle is stationary. The bias drift rate calibration curve is then used to estimate a heading sensor bias periodically while the vehicle is moving. The invention further provides a method for using an aging time for temperature sensor bias drift rate to force convergence of the error variance matrix of the Kalman filter.
In a second aspect, the invention provides vehicle navigational systems that utilize the heading sensor bias drift rate estimated by the methods of the present invention to correct vehicle headings and positions calculated by the dead reckoning system. Preferred embodiments of the navigational systems of the invention comprise a heading sensor, a distance-traveled sensor, a temperature sensor, and a DRS that receives heading and position data from the heading sensor, the distance-traveled sensor, and the temperature sensor, and a computational means for estimating the heading sensor bias drift rate. In preferred embodiments, the heading sensor is a gyroscope. In particularly preferred embodiments, the heading sensor is a low-cost gyroscope.
In a third aspect, the invention provides vehicle navigational systems that utilize the methods of the present invention in conjunction with a vehicle reference position system to correct vehicle headings and positions determined by the dead reckoning component and the vehicle reference position system. In preferred embodiments, the vehicle reference position system is a satellite-based vehicle positioning system. In particularly preferred embodiments, the vehicle reference position system is the global positioning system.
These as well as other features and advantages of the present invention will become apparent to those of ordinary skill in the art by reading the following detailed description, with appropriate reference to the accompanying drawings.